if 2a 3b 17 and 2 a 2 3 b 1..., Surds and Indices, General Mathematics

Question:If` 2^a + 3^b = 17` and `2^(a + 2) - 3^(b + 1) = 5,` the value of a and b respectively are :

A `2, 3` 
B `- 2, 3` 
C `2, - 3` 
D `3, 2`

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+ AnswerD

+ ExplanationGiven equations are :

`2^a + 3^b = 17, 2^2 - 3. 3^b = 5`

`or x + y = 17 & 4x - 3y = 5,` where `x = 2^a  &  y = 3^b.`

On solving, we get : x = 8 and y = 9.

`:. 2^a = 8 = 2^3` and` 3^b = 9 = 3^2`

:. a = 3 and b = 2

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